Maximum speed of a particle in simple harmoni | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The displacement of a particle in simple harmonic motion is $x(t) = A \sin(\omega t)$.The velocity is $v(t) = \frac{dx}{dt} = A\omega \cos(\omega

Vedclass · Accepted Answer

$\frac{2v_{max}}{\pi}$

Vedclass · Answer

(D) The displacement of a particle in simple harmonic motion is $x(t) = A \sin(\omega t)$.The velocity is $v(t) = \frac{dx}{dt} = A\omega \cos(\omega t)$.The maximum speed is $v_{max} = A\omega$.The average speed is defined as the total distance traveled divided by the total time taken.In one complete oscillation,the particle travels from $x = 0$ to $x = A$,then to $x = -A$,and back to $x = 0$.The total distance traveled is $d = A + 2A + A = 4A$.The time taken for one complete oscillation is the time period $T = \frac{2\pi}{\omega}$.Therefore,the average speed $v_{avg} = \frac{	ext{Total Distance}}{	ext{Total Time}} = \frac{4A}{T} = \frac{4A}{2\pi/\omega} = \frac{2A\omega}{\pi}$.Substituting $v_{max} = A\omega$,we get $v_{avg} = \frac{2v_{max}}{\pi}$.

Maximum speed of a particle in simple harmonic motion is $v_{max}.$ Then average speed of a particle in one complete oscillation is equal to

Similar Questions

$A$ particle of mass $5 \ g$ performs simple harmonic motion with an amplitude of $10 \ cm$. Its maximum velocity is $100 \ cm/s$. At what distance from the mean position will its velocity be $50 \ cm/s$?

$A$ particle executing simple harmonic motion starts from the mean position with amplitude $A$ and periodic time $T$. At what displacement is its speed one-fourth of the maximum speed?

$A$ spring executes $SHM$ with a mass of $10\,kg$ attached to it. The force constant of the spring is $10\,N/m$. If at any instant its velocity is $40\,cm/s$,the displacement will be .... $m$ (where amplitude is $0.5\,m$).

$A$ particle executes simple harmonic motion with a periodic time of $0.05 \, s$ and an amplitude of $4 \, cm$. What is its maximum velocity?

Obtain the velocity of a particle executing simple harmonic motion $(SHM)$ by considering the projection of a particle undergoing uniform circular motion.

Vedclass Test Series

Exam Paper Generator

Online Exam Module